Definition 3 (Mixed-Monotonicity  and Decomposition Functions)  [1]},[2]} 
 Consider the dynamical system  with initial state \(x_0 \in \mathbb {I}\mathcal {X}_0 \triangleq [\underline{x}_0,\overline{x}_0]\) :
\(x_t^+=\tilde{f}(x_t,u_t,w_t)\triangleq f(z_t),\) 
